Stereo Matching and Graph Cuts

The stereo matching aims to find corresponding entities between two (or more) images, i.e. entities that are projections of the same 3D object in the scene. Constraints used in stereo matching can be classified into two categories: local constraints, which rely only on a pixel and on some pixels in its surrounding, and global constraints, which must be verified by the whole pixels of a line or of the image. The local methods aim to find a matching for a given pixel without taking into account neighbour pixels correspondences. Global methods try to define a global model of the observed scene and to minimize a global cost function. They try to find the correspondences once for all pixels in one line or for all pixels in the image. Graph cuts techniques have been recently used to solve the stereo matching problem involving global constraints. These methods transform the matching problem to a minimization of a global energy function. The minimization is achieved by finding out an optimal cut (of minimum cost) in a special graph. Different methods were proposed to construct the graph. However, when applied to minimize a global cost function in stereo vision, all of them consider for each pixel, all possible disparities between minimum and maximum values. Our contribution is a new method for constructing a reduced graph: only some potential values in the disparity range are selected for each pixel. These values can be provided by a preliminary matching process using only local constraints. We will detail how this method allows to make wider the disparity range, and at the same time to limit the volume of the graph, and therefore to reduce the computation time. In this chapter, the stereo matching problem is defined. A brief state of the art about stereo matching is presented. The stereo matching can be solved by either local methods or global ones. Among the global methods, we give a short introduction of dynamic programming techniques to be a logic introduction of the Graph Cuts methods. We recall the definition of Graph, flow, cut, and the different algorithms to solve the problem of maximum flow. A general formalism of Relabelling problem is used to express the stereo matching as a minimization of an energy function. The implementation of both complete graph (Roy & Cox, 1998) and reduced graph (our contribution) are detailed. The two methods are compared from experimental results.